People that are political rivals and political enemies of the system will be taken to holding facilities, prisons, or whatever have you, and they will "politely, quietly, and privately, request Euthanasia"
and then it will be done, a Judge will slap a gavel somewhere in a courtroom with basically no one but two lawyers who are also apart of this system and he'll be suicided.
LEGAL killing of your opponents is a dream for the elite, now you can just draw up their own suicide petition, kill them, and no one will dare say you faked it, and he'll be dead.
Covertly killing someone requires far more planning, they can't do it everyone, slip ups can occur, beyond this, the fear of being "suicided" cannot be made public, because the government cannot ever admit to its existence as a threat.
legal euthanasia, with the pretext that they can forge the documents is a way bigger stick to wield, and nothing can be done about it, no slip ups will happen, once your dead, its just documents saying you wanted it to happen, its airtight.
with this they can get rid of as many people as they want, and use it as a fear tool to keep others in line, they can't do that with "a barbel dropped on his head" because no one even believes anyone who says its a government kill.
they need it to be a public topic they can admit happens, but never have to say "we'll kill you".